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arXiv · 1511.06332

A few remarks on the tube algebra of a monoidal category

Sergey Neshveyev·Makoto Yamashita
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Abstract

We prove two results on the tube algebras of rigid C$^*$-tensor categories. The first is that the tube algebra of the representation category of a compact quantum group $G$ is a full corner of the Drinfeld double of $G$. As an application we obtain some information on the structure of the tube algebras of the Temperley-Lieb categories $TL(d)$ for $d>2$. The second result is that the tube algebras of weakly Morita equivalent C$^*$-tensor categories are strongly Morita equivalent. The corresponding linking algebra is described as the tube algebra of the $2$-category defining the Morita context.

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Sergey Neshveyev, Makoto Yamashita. 2015-11-19. A few remarks on the tube algebra of a monoidal category. https://doi.org/10.1017/s0013091517000426

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